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2-2 Comparing and Ordering Rational Numbers
Evaluating
Algebraic Expressions
California
Standards
NS1.1 compare rational numbers in
general.
Also covered: NS1.3
2-2 Comparing and Ordering Rational Numbers
Elbow Partners
Evaluating Algebraic Expressions
Vocabulary
least common denominator (LCD)
Slide Rule
See Green Notebook for definitions
2-2 Comparing and Ordering Rational Numbers
Additional Example 1A: Comparing Fractions by
Finding a Common Denominator
Compare. Write <, >, or =.
Evaluating Algebraic
Expressions
Put
in Notes
5
7
>
6
10
Method 1: Multiply to find a common denominator.
Multiply 6 and 10 to find
6  10 = 60
50
5  10
10
5

=
=
6  10
60
10
6
76
42
6
7

=
=
60
10  6
6
10
50 > 42 ,so 5 > 7
60
60
6
10
a common denominator.
Write the fractions
with a common
denominator.
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Give an example
Evaluating Algebraic Expressions
Remember!
The least common multiple
(LCM) of two numbers is the
smallest number, other than 0,
that is a multiple of both
numbers.
2-2 Comparing and Ordering Rational Numbers
Put in your Notes
Evaluating Algebraic Expressions
To compare or order fractions and decimals,
you need to convert them all to fractions or
all to decimals.
2-2 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions by
Finding a Common Denominator
Compare.
Write <, Algebraic
>, or =.
Evaluating
Expressions
2
4
Put in notes
3
5
Method 2: Find the least common denominator.
List multiples of 3 and
3; 3, 6, 9, 12, 15…
5. The LCM is 15.
5; 5, 10, 15
10
25
5
2

=
=
Write the fractions with
35
15
5
3
>
4
3
4

=
5
3
5
10 < 12 ,so
15
15
3
12
=
15
3
a common
denominator.
2 < 4
3
5
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 1A
Compare. Write <, >, or =.
Evaluating
Algebraic
Expressions
Rally
Coach
1
2
>
2
5
Method 1: Multiply to find a common denominator.
Multiply 2 and 5 to find
2  5 = 10
5
15
5
1

=
=
10
25
5
2
22
4
2
2

=
=
52
10
2
5
5 > 4 ,so 1 > 2
10
10
2
5
a common denominator.
Write the fractions
with a common
denominator.
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 1B
Compare. Write <, >, or =.
Evaluating
Algebraic
Expressions
2
3
Rally
Coach
3
4
Method 2: Find the least common denominator.
>
3; 3, 6, 9, 12, …
4; 4, 8, 12…
8
24
4
2

=
=
12
34
4
3
3
3
3

=
4
3
4
8 < 9 ,so
12
12
3
9
=
3
12
2 < 3
3
4
List multiples of 3 and
4. The LCM is 12.
Write the fractions with
a common
denominator.
Compare the fractions.
2-2 Comparing and Ordering Rational Numbers
Additional Example 2: Comparing by Using
Decimals
Evaluating
Expressions
Compare.
Write <,Algebraic
>, or =.
Put in notes
2
2
_ < 5_
A. 5
9
7
_
_ = 5.285714…
_ = 5.2 and 5 2
5 2
7
9
_
5.2 < 5.285714…, so 5
2
_
9
<5
Write the
fractions as
decimals.
2 Compare the
_
7
decimals.
2-2 Comparing and Ordering Rational Numbers
Additional Example 2: Comparing by Using
Decimals
Evaluating
Expressions
Compare.
Write <, Algebraic
>, or =.
2
B. –0.44 < – _
5
2
2 = –0.4
–_
Write - _
as decimal.
5
5
2
_ Compare the
–0.44 < –0.4, so –0.44 < –
5 decimals.
1 > 0.1
C. _
9
1
1 = 0.1
_
Write _
as decimal.
9
9
Compare the
1 > 0.1
0.1 > 0.1, so _
decimals.
9
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 2
Compare.
Write <,
>, or =.
Evaluating
Algebraic
2
3
_ < 4_
A. 4
9
5
_
3 = 4.6
2 = 4.2 and 4 _
4 _
9
5
Expressions
Rally
Coach
Write the fractions
as decimals.
2
3 Compare the
_
_
4.2 < 4.6, so 4 < 4
9
5
decimals.
2-2 Comparing and Ordering Rational Numbers
Check It Out! Example 2
Compare. Write <, >, or =.
Evaluating Algebraic Rally
Expressions
Coach
4
B. –0.80 = – _
5
4 = –0.8
–_
5
4
Write – _
as decimal.
5
4 Compare the
_
–0.80 = –0.8, so –0.80 = –
5 decimals.
5
_
C.
6
> 0.8
5
Write _
as decimal.
5 = 0.83
_
6
_
6
5 > 0.8
0.83 > 0.8, so _
6
Compare the
decimals.
2-2 Comparing and Ordering Rational Numbers
Example 3
7
The numbers __ , 3.0, –2.2, and –3.9
2
Evaluating Algebraic Expressions
represent the percent changes in
populations for four states. List these
numbers in order from least to greatest.
Place the numbers on a number line and read
them from left to right. Convert to decimals.
7
__
2
3.0
–3.9
–2.2
–5

–4 –3

–2
–1
0
1
2
 
3
4
5
The percent changes in population from least
to greatest are –3.9, –2.2, 3.0, and 7 .
2